Model categories, trivial fibrations and cofibrations l.l.p.

Question

Defintion $\bf 1.1.2~$ Suppose $i:A\to B$ and $p:X\to Y$ are maps in a category $\mathcal C$. Then $i$ has the left lifting property with respect to $p$ and $p$ has the right lifting property with respect to $i$ if, for every commutative diagramm $$\require{AMScd} \begin{CD} A @>{f}>> X\\ @V{i}VV @VV{p}V \\ B @>{g}>> Y \end{CD}$$ there is a lift $h:B\to Y$ such that $hi=f$ and $ph=g$.

---

Definition $\bf 1.1.3~$ A model structure on a category $\mathcal C$ is three subcategories of $\mathcal C$ called weak equivalences, cofibrations, and fibrations, and two functorial factorizations $(\alpha,\beta)$ and $(\gamma,\delta)$ satisfying the following properties:

1. ($2$-out-of-$3$) If $f$ and $g$ are morphisms of $\mathcal C$ such that $gf$ is defined and two of $f,g$ and $gf$ are weak equivalences, then so is the third.
2. (Retracts) If $f$ and $g$ are morphisms of $\mathcal C$ such that $f$ is a retract of $g$ and $g$ is a weak equivalence, cofibration, or fibration, then so is $f$.
3. (Lifting) Define a map to be a trivial cofibration if it is both a cofibration and a weak equivalence. Similarly, define a map to be a trivial fibration if it is both a fibration and a weak equivalence. Then trivial cofibrations have the left lifting property with respect to fibrations, and cofibrations have the right lifting property with respect to trivial fibrations.
4. (Factorization) For any morphism $f$, $\alpha(f)$ is a cofibration, $\beta(f)$ is a trivial fibration, $\gamma(f)$ is a trivial cofibration, and $\delta(f)$ is a fibration

I do not understand the definition $1.1.3.(3)$ in the snippet above:
Does it say that if $f$ has l.l.p. w.r.t. $p$ and $f$ is a trivial cofibration then $p$ is a fibration OR that if $f$ is a trivial cofibration and $p$ is a fibration then $f$ has l.l.p. w.r.t. $p$ ?

Answer 1

It says: Let $f:X'\rightarrow X'$ be a map and $C$ a class of maps suppose that for every element $Y\rightarrow Y'$, of $C$ if there exists a commutative diagram

$$\require{AMScd} \begin{CD} X @>>> Y\\ @V{f}VV @VV{c}V \\ X' @>>> Y' \end{CD}$$

then there exists a map $X'\rightarrow Y$ which make the triangles commute. Then we say that $f$ has the letf lifting property in respect of the family $C$.

Now take $C$ be the class of cofibrations, we obtain that $f$ a trivial fibration. If $C$ is the class of trivial cofibrations we obtain that $f$ is a fibration.